Extension-Torsion-Inflation Coupling in Compressible Magnetoelastomeric Thin Tubes with Helical Magnetic Anisotropy

An axisymmetric and axially homogenous variational formulation is presented for coupled extension-torsion-inflation deformation in compressible magnetoelastomeric tubes in the presence of azimuthal and axial magnetic fields. The tube's material is assumed to have a preferred magnetization direction which lie in the radial plane but at an angle from the tube's axial direction - this imparts helical magnetic anisotropy to the tube. The governing differential equations necessary to solve the above deformation problem are obtained which are shown to reduce to a set of nonlinear algebraic equations in the thin tube limit. This allows us to obtain analytical expressions in terms of the applied magnetic field, preferred magnetization direction and magnetoelastic constants which tell us how these parameters can be tuned to generate unusual coupled deformations such as negative Poisson's effect. The study can be useful in designing magnetoelastic soft tubular actuators.